Britain has a "moral obligation" to help Afghan interpreters who are in danger of being abandoned and hunted down by the Taliban, senior political and military figures have said.

In an open letter, the high-profile names, including former chief of the general staff, Sir Mike Jackson, and Lord Ashdown, said it is shameful that Britain is the only Nato country yet to provide Afghan interpreters with asylum.

The letter, published in the Times on Saturday, said the current system of dealing with asylum claims by Afghans on a case-by-case basis is "slow, not transparent and offers no guarantee of success".

"Afghan interpreters who've stood shoulder to shoulder with our armed forces in Afghanistan are now in danger of being abandoned by Britain," it continued.

"The British military's job in Afghanistan would have been impossible without local interpreters, who have risked their lives and made extraordinary sacrifices just like British soldiers."

The senior figures, who also include Michael Clarke, director of defence thinktank the Royal United Services Institute and former army officer Patrick Hennessy, author of The Junior Officer's Reading Club, added that around 20 interpreters were killed in action, five were killed while off duty, and dozens of others had been injured. With the withdrawal of UK troops, many are left in fear of Taliban reprisals.

The letter follows a growing campaign over rights for Afghan interpreters and their families to settle in Britain.

A petition launched by one interpreter has already gathered more than 60,000 signatures, and the cause has been taken up by campaign group Avaaz.

The man, known only as Abdul to protect his identity, is in hiding in Afghanistan after he and his family were threatened by the Taliban because of the work he did for the British forces.

Last month Avaaz campaign director, Alex Wilks, accused Britain of leaving interpreters behind to be "hunted down by the Taliban".

Leigh Day solicitors, acting for Abdul, have already written to the Foreign Office and the Ministry of Defence asking for the "targeted assistance scheme", which the government provided to Iraqi interpreters employed by the British forces in Iraq, to be extended to Afghans who did the same thing in Afghanistan.

The scheme allows qualifying staff the right either to resettle in Britain or a one-off financial payment.

Last month peers clashed over the issue as the government came under fire from ex-services chiefs, including former first sea lord and Labour peer Admiral Lord West of Spithead, and former chief of the defence staff Air Chief Marshal Lord Stirrup.

Today's letter in the Times says: "After the Iraq war, the UK gave Iraqi interpreters asylum in this country, but – shamefully – Britain is the only Nato country yet to do this for Afghan interpreters.

"Nearly 60,000 Britons have raised their concerns, backing the Avaaz campaign urging British foreign secretary, William Hague, to immediately grant them asylum."

It goes on: "Unlike the Iraqi interpreters, asylum claims by Afghans are currently treated on a case-by-case basis: this process is slow, not transparent and offers no guarantee of success.

"The Ministry of Defence's argument against an Iraqi-style scheme has been that it was 'expensive, complex to administer and took little account of any individual need for protection'.

"Our argument is that Britain has a moral obligation to support this small number of brave men who put themselves in grave danger so that British soldiers could do their jobs."